Jamie Mackie's 64th minute strike gave struggling Plymouth Argyle a fully deserved victory.
Boro still could have salvaged something from the game when awarded a dubious penalty in the 79th minute, when referee Mike Russell felt that Sean St Ledger was brought down by Kari Arnason.
But Adam Johnson wasted the opportunity to score his tenth goal of the season when stroking his spot-kick against the outside of the right-hand post.
It would have been an injustice for Plymouth had Boro levelled because Paul Sturrock's side got stuck in from the start and were the better team over the 90 minutes.
As was expected, Boro started in lively fashion in a bid to impress Strachan.
But they missed a glorious early chance when Marvin Emnes needed one touch too many with the goal at his mercy and Shane Lowry made a blocking challenge.
As the half progressed Plymouth gradually took control and might have led at the interval but for saves by goalkeeper Bradley Jones from Alan Judge and Karl Duguid.
Strachan brought on loan striker Marcus Bent at the start of the second half and it was Boro who had the first chance when a close-range effort from Leroy Lita was blocked on the line by Arnason.
Plymouth were soon pushing forward again and after Alan Gow had fire narrowly wide, Jones made a fine parrying save from Mackie.
But it was no surprise when the visitors went ahead when an error by David Wheater allowed Mackie to run clear and score with a low drive.
Boro should have levelled three minutes later when Bent was presented with a great opportunity from a Julio Arca cross, but headed wide from a few yards.
Boro were then presented with a get out of jail free card when St Ledger seemed fortunate to be awarded a penalty under a challenge from Arnason.
But Johnson spurned the chance and Boro never looked like salvaging anything from the game after that.